44 



ANALYTIC 



fr... III. 



ttona. Moreover, each point of .1/.V has for its abscissa -5, hence 

 oordinates of each of its points satisfy the equation r + 5 = 0. 



In the chosen system of coonli- 



v |t . AT* nates, tin- lint- M\ i- ralle.l tln 



locus of this equation. 



Similarly, the equation x-6 

 =0 is satisfied by any pair of 

 values of which x is 5, such as 



(5,2), ( alltho 



corresponding points lie on a 

 straight line ATN 1 , parallel to 

 the y-axis, at the distance f> from 

 it, and on it> positive side; i.e., 

 M V is the locus of the equa- 

 tion x 5 = <. 



(_') tWrtH the equations y 3 = 0, to find their loci By the same 

 reasoning as in (1) it may be shown that the locus of the equation 

 y + :j = o is the straight line AB, parallel to the x-axis, situated at the 

 distance 3 from it, and on its negative side. Also that the locus of the 

 equation y - 3 = is CD, a line parallel to the x-axis, at the diM 

 3 from it, and on its positive side. 



More generally, it is evident that in Cartesian cm",rdinate (rectangular 

 or oblique), an equation of the first degree, and containing but one variable, 

 represents a straight line parallel to one of the coordinate axes. * 



m the equation 3 x - 2 y + 12 = 0, to find its locus. In this 

 equation both the variables ap|ar. By assigning any definite value to 

 either one of the variables, and solving the equatiou for the other, a pair 

 of values that will satisfy the equation is ob- 

 tained. Thus the following pairs of values 

 are found : 



*, = 0, y, = 6 

 *t = It y = 7J 



** = 2, y s = 



*t 



s. 



-!, y, = 41 



- 2, y, = 3 



- *. y; = 1* 



Plotting the corresponding points 

 /Y /'. /' 4 -,where P l s(x lt y l ) 



(0,6), 



FIG. 16. 



they are all found to lie ou the straight line EF, which is the locus of 

 the equation 3 x - 2 y + 12 = 0. 



